It is known that a polymerization of ethylene can be effected by using a highly active catalyst composed of a solid catalytic ingredient in which a titanium tetrahalide is carried on a magnesium compound and another ingredient which consists of an organic aluminum compound. With respect to the above-mentioned polymerization, various approaches have been attempted to provide a new method which is effective for increasing the yield of the resultant polymer per unit weight of the solid catalytic ingredient in the catalyst used, to such an extent that the resultant polymer contains a very small content of the used catalyst therein and, therefore, an operation for removing the used catalyst from the resultant polymer can be omitted.
For example, Japanese Patent Application Laid-open No. 53-78287 (1978) discloses that ethylene can be polymerized by using a catalyst composed of a solid catalytic component which has been prepared by reacting a magnesium alcoholate with a reaction product of an aluminum halide with a tetraalkoxysilane, and by bringing the resultant solid product into contact with titanium tetrahalide, and another catalytic component consisting of an organic aluminum compound. Also, the above-mentioned laid-open application discloses that the pressure of ethylene in the polymerization procedure is adjusted to 10 kg/cm.sup.2, the yield of polyethylene is about 25,000 g per gram of the solid catalytic component and per hour of the polymerization time. However, in order to produce a polyethylene having a high degree of purity thereof so that the operation for removing the used catalyst from the resultant polymer is unnecessary, it is necessary to increase the yield of the polymer per gram of the used catalyst to more than the above-mentioned yield.